1. Field of the Invention
The present invention relates to a musical sound waveform generator for use in an electronic musical instrument and, more particularly, to a musical sound waveform generator for generating musical sound waveforms containing various harmonic components by use of modulation.
2. Description of the Prior Art
The advances in digital signal processing techniques have enabled a PCM type of electronic musical instrument which is a first prior art of an electronic musical instrument using digital processing. The PCM type of electronic musical instrument can generate musical sound waveforms simple in characteristics. In addition, the PCM type of electronic musical instrument can directly sample sounds generated by conventional or traditional musical instruments, sounds generated by humans and sounds generated in the natural world (hereinafter they are referred to as natural sounds) to store them and reproduce them at arbitrary pitches.
A second prior art of an electronic musical instrument capable of generating musical sound waveforms having various kinds of complex characteristics in a digital manner is an electronic musical instrument using an FM method which is disclosed in a Japanese Examined Patent Publication No. 54-33525 or a Japanese Unexamined Patent Publication No. 50-12640.
This type of electronic musical instrument generates a musical sound waveform e which is given by EQU e=A.multidot.sin{.omega.ct+I(t)sin.omega.mt} (A)
By selecting a carrier waveform frequency .omega..sub.c and a modulation waveform frequency .omega..sub.m for modulating the carrier waveform frequency .omega..sub.c in an appropriate ratio and setting a time-varying modulation index I(t) and a time-varying amplitude coefficient A, it is possible to obtain very individual synthetic musical sounds having complex and time -varying harmonic characteristics.
A third prior art of an electronic musical instrument, which is improved over the FM type of electronic musical instrument, is disclosed in a Japanese Examined Patent Publication No. 61-12279. This type of electronic musical instrument employs an arithmetic operation using a triangular waveform in place of the arithmetic operation using a sine waveform as indicated in equation (A). Namely, an output musical sound waveform e is given by EQU e=A.multidot.T{.alpha.+I(t)T(.theta.)} (B)
where T(.theta.) is a triangular function which is produced by a modulation wave phase angle .theta.. By advancing a carrier wave phase angle .alpha. and the modulation wave phase angle .theta. in an appropriate proceeding speed ratio and setting a modulation index I(t) and the amplitude coefficient A as in the case of the first prior art, it is possible to synthesize a musical sound waveform.
In view of such prior arts as described above, electronic musical instruments have been called upon recently to have a capability of dynamically generating various types of sounds including musical sounds which are very peculiar to electronic musical instruments and natural sounds.
However, the PCM type of electronic musical instrument, which is the first prior art, is very good at generating natural sounds themselves but is poor at processing the natural sounds so as to obtain individual tone colors.
That is, with the PCM type of electronic musical instrument, in order to continuously change an original sound to a sine waveform by way of example, digital filters or analog filters are used to eliminate harmonic components of the original sound. The digital filters will inevitably become relatively large in circuit scale. Furthermore, to vary the characteristics of the digital filters with a time-varying function such as an envelope, it is required to store filter coefficients corresponding to the filter characteristics in addition to data on natural sounds. With the analog filters, on the other hand, desired characteristics are difficult to obtain. In addition, a time-division operation for generating a plurality of sounds simultaneously cannot be performed.
Furthermore, where, in contrast to the above, it is desired to continuously change an original sound to a musical sound with a more complex harmonic structure, the system using filters for eliminating harmonic components of the original sound cannot produce new harmonic components.
A musical sound generated by an actual musical instrument such as a piano contains not only a fundamental wave component having a pitch frequency but also a plurality of harmonic components having frequencies which are integral multiples of the pitch frequency. The musical sound can contain up to fairly high harmonic components. In addition, the musical sound may contain harmonic components whose frequencies are non-integral multiples of the pitch frequency. The proportion in which each of the harmonic components is contained in a musical sound differs according to the kinds of musical instruments, and there are as many harmonic characteristics as there are the kinds of musical instruments. In this way musical sounds with a rich tone quality are produced by virtue of harmonic components inherent in each musical instrument. The second or third prior art electronic musical instrument based on the FM method is very good at processing of the harmonic structure of a musical sound to be generated. However, it is difficult to set optimum parameters for generating a desired musical sound peculiar to each musical instrument.
That is, since the second prior art is based on sine wave modulation, a musical sound generated in accordance with equation (A) has its frequency components concentrated on lower harmonic components (low in frequency). Thus, even if the modulation index I(t) is made large in value for a deep modulation, higher harmonic components (high in frequency) cannot be produced well. With the second prior art, therefore, musical sounds with rich tone qualities as in actual musical sounds cannot be generated and the tone qualities of musical sounds that can be generated are limited.
In contrast to the second prior art, the third prior art using equation (B) is based on a modulation system using a triangular wave, which contains many harmonics from the beginning, and thus can easily generate a musical sound which definitely contains up to higher harmonic components for the time being. In order to obtain a desired musical sound as an output, it is difficult to set the proceeding speed ratio of the carrier wave phase angle .alpha. to the modulation wave phase angle .theta., the modulation index I(t) and the amplitude coefficient A in equation (B) most appropriately. In addition to this, the third prior art, which drives a triangular wave with a triangular wave, cannot realize a process during which the harmonic components of a musical sound sequentially decay beginning with the highest harmonic component and finally only a single sine wave component corresponding to the pitch frequency remains while the musical sound gradually decays after it has been generated.
Furthermore, in a case where a musical sound waveform to be obtained varies with time after its generation, it is difficult for each of the second and third prior arts to set parameters so as to produce a desired waveform varying with time.
For example, a piano can generate a musical sound which contains many higher harmonic components and which provides a feeling of hardness when a key is depressed strongly and a musical sound which contains almost only a single sine wave component and which provides a feeling of softness if the key is depressed very weakly. Also, the piano can generate musical sounds which contain many higher harmonic components when depressing low-tone keys and musical sounds which have few harmonic components by depressing high-tone keys. In this way the characteristics of musical sounds can be controlled in accordance with performance information at the time of performance operation. However, since the first prior art has difficulty in controlling harmonic components as described above, the above effects are also difficult to realize. Also, with the second prior art, even if the modulation index I(t) can be controlled to a large value, there are limitations on the level of higher harmonic components that can be generated. Thus, it is impossible to generate a musical sound which contains higher harmonic components richly according to a performance operation. Moreover, with the third prior art, in a case where the key is operated very weak, even if the modulation index I(t) can be controlled to a small value (for example, 0) according to such performance information, it is impossible to control so as to allow a single sine wave component to be generated. Namely, the third prior art has a problem that a musical sound with a feeling of softness, which contains only a single sine wave component, cannot be generated according to a performance operation.
With the electronic musical instrument of the PCM type, the so-called loop reproduction is generally performed in which a specific waveform period of a natural sound is reproduced from a memory repeatedly in order to economize the storage capacity or to reproduce a sustained sound. However, the mere loop reproduction will always reproduce musical sounds of the same characteristics of the waveform period. In this case, even if the amplitude envelopes are allowed to be varied, monotonous musical sounds will result because tone colors themselves do not vary. Having difficulty in processing natural sounds as described above, the PCM type of electronic musical instrument has difficulty in adding tone color variations at the time of the loop reproduction as well.
In general, acoustic pianos and so on have a considerable difference in tone color between when low note keys are depressed and when high-note keys are depressed or when keys are depressed strongly and when keys are depressed weakly. To realize such a difference in tone color by means of the PCM system, data have to be stored for each of tone colors, causing a considerable increase in cost. Having a difficulty in processing the characteristics of musical sounds as described above, the PCM system also has a problem that it is further difficult to generate a musical sound having its characteristic varied continuously between high and low frequency ranges by way of example.